Question

Solve algebraically
8x + 4y = 48
12x + 5y = 21

Answer 1

Answer:

$x=-\frac{39}{2}\\ y=51$

Step-by-step explanation:

$8x+4y=48\\12x+5y=21$

Let's solve the first equation for x or y. I'll do it for y.

$8x+4y=48$

Subtract 8x

$4y=-8x+48$

Divide by 4.

$y=-\frac{8}{4}x+\frac{48}{4}$

Simplify.

$y=-2x+12$

Now replace the value of y in the second equation for this.

$12x+5y=21\\12x+5(-2x+12)=21$

Distribute 5

$12x-10x+60=21$

Subtract 60

$12x-10x=21-60$

Combine like terms;

$2x=-39$

Divide by 2.

$x=-\frac{39}{2}$

Now replace this in any of the equations to find the value of y.

$8x+4y=48\\8(-\frac{39}{2})+4y=48$

8 and 2 can be simplified.

8/2=4

2/2=1

$4(-39)+4y=48$

Distribute 4.

$-156+4y=48$

Add 156

$4y=48+156\\4y=204$

Divide by 4

$y=\frac{204}{4}$

$y=51$

Proof:

$8x+4y=48\\8(-\frac{39}{2} )+4(51)=48\\4(-39)+204=48\\-156+204=48\\48=48$

Answer 2

8x+4y=48
-4y -4y
8x=48-4y
divide 8 to both sides

x=6-1/2y


substitute the given value of x into the equation 12x+5y=21

12(6-1/2y)+5y=21

distribute 12 through the parentheses

72-6y+5y=21

add like terms

72-y=21

move constant to the right hand side and change signs

-y=21-72

calculate the difference

-y= -51

change signs

y=51

solve the question for x

x= 6-1/2 x 51

x= -39/2

(x,y) = (-39/2 , 51)